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1 Bernays Project: Text No. 10 The Basic Ideas of Friesean Philosophy in Relation to Contemporary Science (1930) Paul Bernays (Abhandlungen der Fries schen Schule, New Series 5 ( ), no. 2 (1930), Title on a separate page (p. 97), tract iv. On p. 98: Talk, delivered to friends of the Friesean School on 10 August 1928 in Göttingen. ) Translation by: Volker Peckhaus Comments: Revised by Paolo Mancosu and Steve Awodey 99 Dear schoolmates! In having the honor to speak in the context of a meeting devoted to the memory of Leonard Nelson, I would like first to set forth briefly the purpose of my presentation. Nelson was the appointed head of his school not only because of the sharpness of his thought but also on account of his overall personality. Such a personality gathers among its followers people who in part differ very widely in their opinions, each of whom takes from the whole of the philosophical doctrine what for him is essential in this doctrine. This fact makes itself felt when such an intellectual leader passes away. For the members of the school, 1

2 and indeed for every single one of them, the question arises in what manner he should preserve and elaborate the received thoughts for himself, and also how to further bring them to bear outwardly. In our case this question arises all the more as Nelson s system of thought is devoted to the reawakening and further elaboration of a philosophy which one had more or less considered wrapped up; and it arises all the more as in this philosophy the work of a philosopher has already been elaborated by a thinker differing in many respects, as Fries did in comparison to Kant. 100 Each of us can answer this question only for himself. However, allow me to propose certain ideas in this respect, whereby I do not make any claim to a complete treatment of the topic, if only for the reason that I will speak here only about questions concerning the critique of knowledge. I would like to stress a certain, uniform complex of thoughts of the Kant-Friesian school which seems to me, in any case, to retain its important role in philosophy. As you know, there is a certain discrepancy between several claims of the Kant-Friesian philosophy and present-day scientific theories. This discrepancy is very clear and coarse. But it is not that striking that many things in present-day science develop in such a way that makes it possible, if stressed in the proper way, to bring to bear the thoughts of the Kant-Friesian philosophy again, provided only that one is prepared to make certain modifications to it. Above all I mean those thoughts that constitute transcendental idealism and the difference between intuitive knowledge and purely conceptual knowledge. If we consider the most recent philosophical doctrines, we find that most 2

3 of them oppose transcendental idealism in principle. It is especially the philosophy of immanence of Mach s school that is widespread among researchers in the exact sciences and indeed it dominates almost absolutely. This philosophy claims to be able to eliminate the notion of existence in general and to get by with the notion of phenomenon. According to it, there is fundamentally no other kind of knowledge than perceiving, remembering, following the sequence of representations and comparing the contents of representation. 101 The difficulties of this position are known to you. I need not consider them more closely. I would only like to point out that W. Freytag in his book Realism and the problem of transcendence (Halle 1902) explains very well the weaknesses of the position of immanence. M. Schlick also follows this book in certain parts of his General Theory of Knowledge (Berlin 1918); however, he again slips back into the position of immanence in another way when characterizing cognition as recognition from the outset, thus restricting cognition again to a mere comparison of the given. Phenomenalism has received certain refinements. One of these is found today in the Russellian school of mathematical logic. Here the domain of the intuitively given is enlarged by certain logical constructions. It is characteristic in this connection that one essentially deals here only with class constructions, that is only with an abstract kind of comparison. What is united into classes are either contents of representations or classes already constructed. In principle one does not go with this beyond phenomenalism, for Mach and his school as well have considered the construction of concepts as essential in addition to direct intuitive representations. 3

4 But the tendency to a restriction to the immanent is quite widespread not only in those approaches to philosophy that are tied to the exact sciences but also in the philosophy characterized as spiritual. An especially remarkable and engaging form of the standpoint of immanence is that adopted in Husserl s phenomenological school. There 102 the principle of displayability of every single phenomenon is posed as a methodological guideline, i. e. the requirement that every concept or term introduced be justified by displaying a phenomenon determined by it. If this principle is understood in a sufficiently wide sense, there is nothing to object against it. But there is the obvious interpretation, and it is applied by many followers of the school, according to which our reasoning has to remain in the domain of phenomena, i. e. contentual representation, that therefore nothing beyond the given can be reasonably thought of at all. By the way, it is remarkable that Oskar Becker in his book Mathematical existence (Halle 1927) recently called this standpoint transcendental idealism. Among the philosophical directions known today there is arguably not a single one that is opposed to the positions just mentioned as fundamentally as the doctrine of Fries. Fries laid stress on exactly what all these philosophers endeavor to argue away, namely the fundamental transcending of the contentual standpoint by the forms of thought. The categorial formation of the judgment can only be understood as the expression of a demand of cognition, as expression of a search, guided by a belief that is already inherent opaquely in every perception and generally in every state of consciousness, but which makes itself explicit in a clearer form only through thought. This belief gives us the conviction that the contents found in experience are to be 4

5 related to a reality, to a unity of existing objects, that is in itself real and structured into real connections. It can be explained why one has serious problems in making up one s mind to accept this doctrine. First of all, one would like to have a standpoint with as few presuppositions as possible, and with the assumption of 103 the rational belief too much seems to be postulated at the outset. Upon closer examination, this objection does not apply to the Friesian doctrine of conceptual knowledge as such, but to the view that the content of this knowledge can be rendered in entirely distinct, definitely formulated principles. Anyway, I would like to point out that the fundamental idea of the Friesian doctrine is by all means compatible with the fact that the way in which, in the investigation of nature, we relate the contents of experience to existing objects by reasoning is not determined in knowledge but belongs itself to the task of research that is given to us by reason. There is however another reason for the resistance against the Friesian doctrine. I leave out of consideration here the known difficulties related to the question of the correct characterization of the mode of existence of reason and its expressions. It has been very much discussed, especially in our school, whether conceptual knowledge has to be regarded psychologically as a faculty or as a continuous activity. These are difficulties and problems but not really objections; they are objections only for the one who, again in the domain of psychology, intends to carry out the standpoint of a complete restriction to contents. Fries thought in this respect more vitally; he did not want to be content with a theory of psychological phenomena, but aimed at a theory of the unit of life; and I think we have reason to agree with him in this 5

6 respect. What forms, however, a more substantial reason for the resistance against the Friesian claims is that on closer inspection one recognizes that one is thereby already necessarily pushed towards transcendental idealism. Because in the fact that conceptual knowledge makes itself felt in the form 104 of a categorial requirement of an existential relation (otherwise no more precisely determined) to a world of existing, there lies already the division of truth. Both the contentual and the categorical form belong to knowledge as such. According to the position of naive realism we believe to find both united and to have in common perception complete knowledge before us. Closer inspection forces us in a well-known way to give up this position; it becomes manifest to us that the experiential uniform perception consists of two distinct parts in regard to knowledge: the givenness of a contentual material and the existential reference to the unity of reality in which the former has to be integrated in a manner initially unknown. The fundamental imperfection of our knowledge is based on this. We know the contents of our experience and can talk about them; but how to interpret them as proper truth is only very fragmentarily known, although to an extent that is sufficient for the purposes of our practical standards of living, within which we help ourselves with a general attitude based on beliefs in those domains where our scientific knowledge no longer suffices. If we introduce transcendental idealism that way independently from the doctrine of antinomies we can thereby remain in complete agreement with Fries. For the doctrine of the division of truth, which Fries subsequently puts forward for the resolution and explanation of the antinomies, does not need the antinomies for its grounding. And this is a methodological advan- 6

7 tage, since the doctrine of the antinomies contains very many problematic arguments. Above all there is the risk of proving too much 105 by posing statements in the antithesis that are by no means irrevocable in principle for scientific thinking and therefore assign boundaries to science, which in fact it does not have. Transcendental idealism must not be understood in such a way that it produces a factual-structural discrepancy between what is given in reality and what is asserted in the scientific world view. If science has to have meaning we have to hold the standpoint that what is claimed in science as factual as far as it is not a common error in the sense of science itself also expresses a fact of reality, and in any case it does not deviate from reality in such a way that is expressible in the framework of science itself. The limitation of scientific knowledge has therefore to be based in a proper sense on the conditions of possibility of the scientific investigation of nature as such. Such a condition is, in the first place, the connection to perception. The considerations which force us to give up naive realism and in general to eliminate sensible qualities in the physical reflection have to be imputed to the antinomies. The discursive character of science is a further essential condition that comes from the fact that conceptual knowledge is conveyed to us through thought. In fact even here something arises which in any case is inadequate to reality, namely the hypothetical form of the laws of nature. It is not in accordance with the idea of a real connection that the latter consists in a law according to which something takes place under certain circumstances. Such a law can only be a reason but not a real cause. Thus, while 106 the aforementioned antinomy refers to the fact that we don t have 7

8 knowledge of existing in its essence but only as something that stands in certain relations, the second antinomy concerns the lack of essence of the connection. The existence of still other antinomies, especially of the kind posed by Kant, should in no way be disputed in principle. But in any case a revision of the given, which goes farther than what has been carried out so far in our school, is necessary. If we observe how factual natural science relates to the program of pure immanence we find that one has departed from the observance of a phenomenological program more than ever, despite the conscious emphasis on Mach s thoughts, which were also propounded in particular by Einstein. There we have completely abstract existence claims, which are related to perception only in their consequences. This is especially true for presentday quantum theory. According to this theory the physical state is related to perception only through probability statements, i. e. the physical states whose temporal connection is a wave-theoretical causal one have relevance for perception only through the fact that they involve certain discrete processes in a statistical frequency, computable from the state variables, and these frequencies and also other quantitative determinations of those processes present themselves for the experiment through intuitive quantities, e. g., color and intensity of spectral lines. Likewise, Einstein s general relativity theory by no means conforms to the tendencies of a pure phenomenalism. 107 The lawfulness of the space-time manifold is here introduced purely conceptually through the assumption of a metric field that forms a physical object analogous to the electromagnetic field. The quantitative distribution of this field is correspondingly deter- 8

9 mined by spatio-temporal measurements, similarly to the way the shape of the earth is determined by measurements of lengths on the base of our ordinary intuition of space. However, whereas the earth transcends our power of imagination only because of its size, the metric field is in principle out of the range of the intuitively imaginable on account of the union of the spatial and the temporal which takes place in it. The establishment of such theories, which are very far removed from observation, speaks very strongly in favor of the Friesian doctrine of only conscious conceptual knowledge. Sure enough, these theories cannot be reconciled with the Kant-Friesian doctrine of pure intuition. But we do not need, also in this case, to give up this doctrine as a whole in order to stay in harmony with contemporary scientific theories, but only its specific formulation. Thus, one rightly disputes the Kantian claim that geometry and physics are bound by the framework of our intuitive representations of space and time as a condition of possibility of scientific knowledge. In fact, in its abstractions geometry goes far beyond the framework of the intuitive representation of space by having developed into a general theory of ordered manifolds endowed with topological relations within which the laws of Euclidean geometry form only a special structural lawfulness distinguished by systematic advantages. 108 Moreover, concerning theoretical physics, its recent development has shown with full clarity that the possibility of theoretical knowledge of nature is completely independent from the acceptance of a determinate structural lawfulness of space and time. 9

10 In another respect, however, the Kantian doctrine of pure intuition has curently again gained recognition. For a long time heretofore, the dominant opinion was that mathematics could be developed purely out of logic. The attempt to carry out this idea, as it was initially undertaken by Frege and then by Whitehead and Russell has not succeeded, regardless of the systematic unity of the work Principia Mathematica. Rather, the investigation of the foundations of mathematics has shown two things. First, that a certain kind of purely intuitive knowledge has to be taken as a starting point for mathematics; indeed, that even logic as the theory of judgments and inferences cannot be developed without appealing to such an intuitive knowledge to some extent. It is an issue of the intuitive representation of the discrete from which we draw the most primitive combinatorial representations, in particular that of succession. Constructive arithmetic develops by means of this elementary intuitive knowledge. Secondly, it appears that constructive arithmetic is not sufficient for the theory of real numbers, that rather for the latter we have to add certain notions related to the totality of collections of mathematical objects, e. g. the totality of all the numbers and the totality of all sets of numbers. 109 It is now remarkable that Fries in his Mathematical Philosophy of Nature (Heidelberg 1822) already separated the elementary kind of mathematical knowledge under the name syntactics from arithmetic in the sense of a theory of quantities. He says about syntactics: It contains the most general abstraction which can be done for mathematical knowledge whatsoever. It is solely based on the postulates of the arbitrary order of given elements and their arbitrary repetition 10

11 without end. It has no proper theory, for it does not know any axioms; its operations are for themselves immediately comprehensible... (p. 70) In his considerations on syntactics, however, Fries only thought of the doctrine of permutations and combinations, whereas he treated number theory only in connection with Analysis. He stated: the purpose of the number system is generally to reduce the knowledge of quantity to concepts, i. e. to recognize the relationships between quantities not only intuitively but also through thought. (p. 121) The specific pure intuition of arithmetic is the continuous series of the larger and the smaller. By scientifically developing this pure intuition we should think the idea of quantity or reduce it to concepts. (p. 77) In order to pass from these Friesian views to a conception in accordance with the present state of research one does not need very substantial modifications. Of course, we have to include elementary number theory in the domain of syntactics. Moreover, it cannot be taken for granted that the scientific development of the concept of quantity consists only in the clarification of pure intuitive knowledge. Rather, we have to take the possibility into account that we are dealing here with a conceptual sharpening, 110 an idealization as Felix Klein called it of the intuitive representation of the larger and the smaller. Even so, the rational element would not yet have been excluded from the arithmetical theory of quantities (of Analysis). This is because that conceptual sharpening takes place, as already said, by including certain representations of totality, and thereby we would have to see what reason adds to the intuitive representation. This is supported especially by the fact 11

12 that the representations of totality applied in Analysis become relevant to the system of mathematics by making possible the unrestricted application of the logical forms of the general and the particular judgment in the domain of real numbers and functions. And according to Fries the logical forms of judgments are exactly those through which we become aware of conceptual knowledge in thought. In the sense of such a conception, Analysis would already contain a component of conceptual knowledge grasped only by thought. It would thus have the same epistemological character that Fries assigns to pure natural science, and indeed, in contemporary science, mathematics has entirely the role of pure natural science, the armory of hypotheses, as Fries puts it. It is also characteristic that right from the beginning of the rigorization of infinitesimal methods some sort of phenomenological opposition arose against the rational element in Analysis. At first Kronecker and at present Brouwer and his school propound a position that calls for the restriction to the intuitively representable and according to which the totality assumptions of Analysis mentioned above are categorically rejected. Lately Weyl has hinted at the analogy between this 111 Intuitionism and Mach s standpoint. Hilbert shows, in a completely different way than this opposition, the relevance of his proof theory for the special epistemological position of elementary intuitive (syntactical) or, as Hilbert calls it, finitist mathematics, vis-à-vis systematic mathematics, based on concept formations, in particular Analysis and Set Theory. Hilbert here subjects systematic mathematics to a sort of critique of proof by which, using elementary finite methods, the deductive consequences of the concept formations of systematic mathematics are inves- 12

13 tigated, whereby the aim is to show that the application and the pursuit of these concept formations can never lead to discrepancies in the consequences and thus also, in particular, that it cannot lead to contradictions with the elementary intuitively recognizable facts. For a philosophical completion of this proof theory a methodological explication is necessary by which those principles systematized in proof theory receive some kind of deduction in the sense of a clarification of their epistemological methodological significance. This explication should at the same time clarify the methods of mathematical idealization and with this give a satisfying answer to Nelson s question, what the norm for an idealization could consist, if it does not lie in pure intuition. In conclusion, I would still like to indicate how the special status of aesthetics becomes understandable through the doctrine of transcendental idealism. In the language of our school the expression aesthetic is used for all those objective evaluations, whose measure cannot be conceptually grasped. It 112 appears to be appropriate on the one hand with respect to the ordinary use of language and also for pointing out essential differences to restrict the use of the word aesthetic to that kind of evaluation in which an object is valued as a symbolical representation for something which is not directly accessible to our finite knowledge of nature. According to this, the value of an aesthetic object as such does not attach to the thing as actually existing, as in the case of the value of a noble character whose existence has value for itself, but rather that value is principally related to the representing subject, i. e. the object is only valuable as represented. The objective character of an aesthetic value consists in the objective determination of the 13

14 suitability of an object to serve as a symbolic expression. The interest for such a symbolic expression depends essentially on the imperfection of our view of nature, i. e. the division of truth. We value the symbolic expression of ethical values in the beauty of figures of nature and art, because we cannot directly intuitively represent the value of a being but only assign it conceptually. Likewise, we value the conceptual unity of scientific systems of thought as a surrogate for an immediate intuitive grasp of the unity in the connection of the real. According to this view, theoretical science has leaving out of consideration its vital significance for our orientation and our action an esthetical significance, in so far as we regard it solely under a systematic viewpoint. This conception indeed remains as the only option, if we do not want to exaggerate the role of exact sciences to that of a perfect worldview, or reduce it to 113 that of a mere tool. Accordingly, the scientific systematization has not only the purpose of saving labor, but also an esthetic task that is given to us by reason. Only the doctrine of the belief of reason makes the search for a systematic unity and the success of such a search understandable; from Mach s standpoint this success is a pure miracle. On the other hand, from the doctrine of transcendental idealism we take the advice to moderate our expectation of a systematic completeness in the knowledge of nature. With this I have sketched in what sense I think possible a vital preservation and continuation of the basic thoughts of the Friesian doctrine. You know that it was Nelson s special concern to ensure that the thoughts of Fries s philosophy would not be forgotten again. I believe that one also has to avert another risk, namely that these thoughts, although preserved in the 14

15 tradition, be considered only from a historical perspective and not as standing in vital interaction with philosophical intellectual life. The purpose of my presentation was to show that the Friesian doctrine is capable of such a lively interaction with contemporary philosophy and that we do not need to worry that the basic ideas of this doctrine will be lost by modifications that take into account the development of science. Let us also take into consideration that it was Nelson s own intention to tackle, after completion of his system of ethics, the domain of speculative philosophy, and with this in particular, the philosophical methodology of natural science in the sense of a revision and a new treatment of Fries s thought. 15

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